We don't measure temperature based on feelings. The real temperature is often observed with thermometers (which do not transmit any moisture through the glass, so humidity is not even relevant here), relying upon heat transfer from/to the surrounding air to make the measuring medium (like liquid mercury) expand and contract.

The difference that you feel with humidity, and what the weather stations are trying to say, is that when there is more water in the air it becomes harder for you to cool off and regulate your body temperature. We rely on our ability to sweat, and for that sweat to quickly evaporate, to keep our internals at a comfortable level when we are exposed to heat.